Slurry flow measurement using Coriolis flowmeters incorporating analytical and data-driven modelling

Coriolis flowmeters are effective for single-phase flows; however, their accuracy degrades in case of multiphase flows. Slurry is a complex multiphase flow and limited studies have been conducted for slurry flow metering using Coriolis flowmeters. In this study, a review of the existing slurry flow measurement techniques is given, together with the associated technical issues of Coriolis flowmeters for slurry flow metering. Phase decoupling and asymmetric damping are identified as the significant factors contributing to measurement inaccuracies in Coriolis flowmeters for slurry flow measurement. This study proposes an analytical model that studies the most significant forces acting on the solid particles of two-phase slurry while flowing through Coriolis tubes. Based on the force analysis a decoupling ratio equation is proposed. An error compensation scheme is then developed by combining the decoupling ratio and asymmetric damping effect of slurry on Coriolis tubes for slurry flow metering. This study also presents data-driven models that are incorporated into Coriolis flowmeters for mass flowrate, density and solid volume fraction (SVF) measurement of slurry. Three different data-driven models based on support vector machine (SVM), artificial neural network (ANN), and Gaussian process regression (GPR) are established through training and testing. To examine the behaviour of Coriolis flowmeters under slurry flow conditions, a laboratory scale slurry flow test rig has been upgraded. A series of experimental tests were performed on the test rig for a range of mass flowrates (5,435-18,582 kg/h) and SVFs between 0% and 4.8%. The effects of Coriolis tubes geometry and orientation conditions are also examined by installing two Coriolis flowmeters on horizontal pipe sections with their measuring tubes in upward and downward orientations. Negative errors were observed up to -3.4% and -5.8% for mass flowrate and density measurement of slurry for both orientations, respectively. This also agrees with the theoretical analysis of decoupled motions between solid and liquid phases. Additional factors leading to measurement errors, including density difference, asymmetry, damping, Coriolis tube geometry, and orientation conditions, are also practically evaluated. Experimental results revealed that the proposed analytical model yields a relative error within ±0.5% and ±1.3% for mass flowrate and density measurement of slurry for both orientations of Coriolis flowmeters, respectively, under all test conditions. The performances of SVM, ANN, and GPR models are also assessed in comparison with the reference readings. A data augmentation technique is also applied to generate unseen condition data with ±5% deviation from the original data. The experimental results show that the GPR models are superior to the SVM and ANN models in terms of measurement accuracy. For GPR models, the majority of errors are within ±0.2% while the rest of them are no greater than ±0.6% for mass flowrate, density and SVF measurement of slurry for both original and augmented data, respectively. Finally, it can be concluded that this research outcome has effectively extended the applicability of Coriolis flowmeters to two-phase slurry flow measurement.